{"paper":{"title":"A new interpretation of the Racah-Wigner $6j$-symbol and the classification of uniserial $sl(2)\\ltimes V(m)$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Fernando Szechtman, Leandro Cagliero","submitted_at":"2012-02-01T01:02:16Z","abstract_excerpt":"All Lie algebras and representations will be assumed to be finite dimensional over the complex numbers. Let $V(m)$ be the irreducible $\\sl(2)$-module with highest weight $m\\geq 1$ and consider the perfect Lie algebra $\\g=\\sl(2)\\ltimes V(m)$. Recall that a $\\g$-module is uniserial when its submodules form a chain. In this paper we classify all uniserial $\\g$-modules. The main family of uniserial $\\g$-modules is actually constructed in greater generality for the perfect Lie algebra $\\g=\\s\\ltimes V(\\mu)$, where $\\s$ is a semisimple Lie algebra and $V(\\mu)$ is the irreducible $\\s$-module with high"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0066","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}